1.

Let bar(a), bar(b), bar(c), bar(d) be the position vectors of A, B, C and D respectively which are the vertices of a tetrahedron. Then prove that the lines joining the vertices to the centroids of the opposite faces are concurrent. (This point is called the centroid of the tetrahedron)

Answer»

`BAR(a)+bar(B)=bar(C)+bar(d)`
`bar(a)+bar(b)=bar(c)+bar(d)=bar(0)`
`bar(a)+bar(c)=bar(b)+bar(d)`
`bar(a)+bar(c)=bar(b)+bar(d)=bar(0)`

ANSWER :C


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